Impact of Different Aerodynamic Optimization Strategies on the Sound Emitted by Axial Fans
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19th AIAA/CEAS Aeroacoustics Conference (34th AIAA Aeroacoustics Conference), 27 - 29 May 2013, Berlin Impact of Different Aerodynamic Optimization Strategies on the Sound Emitted by Axial Fans Konrad Bamberger1 and Thomas Carolus2 Institut für Fluid- und Thermodynamik, Universität Siegen, Paul-Bonatz-Str. 9-11, 57068 Siegen, Germany The correlation between the aerodynamic design strategy and the sound emission of low pressure axial fans is investigated by a case study. The four fans investigated are equal in terms of total-to-static design point, rotational speed, diameter, and tip clearance, but different regarding hub size and blade geometry. One fan (the baseline) is designed using the analytical blade element momentum method whereas the other fans are optimized by stationary CFD simulations embedded in an evolutionary optimization algorithm. Three different target functions are applied: Maximization of total-to-static and total-to-total efficiency at design point, and maximization of operating range. The distinction between the two efficiencies addresses two competing effects: While the fan optimized with respect to total-to-total efficiency has the lowest secondary flow effects, its aerodynamic load required to fulfill the same total-to-static pressure rise is higher. The characteristic curves of each fan are measured on a chamber test rig to validate the CFD results. The acoustic investigations are conducted in a semi-anechoic chamber. It is found that optimization with respect to total-to-total efficiency, i.e. minimization of losses, leads to the lowest sound power levels around the design point at low Mach numbers while the design optimized with respect to total-to-static efficiency is superior at high Mach numbers. The fan optimized with respect to operating range is loudest at the design point, but this observation inverses when moving to off-design flow rates. It is concluded that none of the design strategies can be recommended purely from an acoustical point of view and that there always is a trade-off between noise, power consumption, operating range, and development cost. Nomenclature Symbols D = fan diameter LW = sound power level Ma = mach number P = power S = tip clearance T = time V = flow rate a = speed of sound c = chord length d = max. thickness (of NACA airfoil) f = frequency or max. camber (of NACA airfoil) n = rotational fan speed p = pressure w = relative flow velocity x = coordinate along airfoil chord z = number of blades = angle of attack or acoustic exponent = flow coefficient 1 Ph.D. student. IFT, Department Maschinenbau, Universität Siegen, [email protected]. 2 Professor. IFT, Department Maschinenbau, Universität Siegen, [email protected]. 1 American Institute of Aeronautics and Astronautics 19th AIAA/CEAS Aeroacoustics Conference (34th AIAA Aeroacoustics Conference), 27 - 29 May 2013, Berlin = efficiency = sweep angle = hub-to-tip ratio = density = pressure coefficient Subscripts 0 = reference 1 = plane upstream of fan blade 2 = plane downstream of fan blade ac = acoustic d = design h = hub n = normal o = overall s = sampling spec = specific t = total ts = total-to-static tt = total-to-total Abbreviations BEM = blade element momentum method BPF = blade passing frequency CAA = computational aeroacoustics CFD = computational fluid dynamics DES = detached eddy simulation GGI = general grid interface LES = large eddy simulation OOR = optimized for operating range OTS = optimized for total-to-static efficiency OTT = optimized for total-to-total efficiency RANS = Reynolds-averaged Navier-Stokes SAS = scale adaptive simulation URANS = unsteady Reynolds-averaged Navier-Stokes I. Motivation and Objectives he main objectives in the design of axial fans are high energy efficiency and low noise emission over a large T operating range. However, present optimization efforts mainly focus on efficiency whereas noise is often neglected. This originates from the immense difference between prediction of aerodynamic performance and sound in terms of computational cost. Sound prediction by means of computational aeroacoustics (CAA) is generally conducted in two steps. Firstly, the acoustic sources, i.e. the unsteady pressure fluctuations on the fan blade are computed by transient computational fluid dynamics (CFD). Subsequently, the acoustic propagation is computed, e.g. using the Ffowcs Williams and Hawkings1 analogy. This approach was taken by Reese2 who compared the accuracy in terms of acoustic source prediction of four distinct unsteady CFD methods: URANS, SAS, DES, and LES. The best results were obtained by LES (large eddy simulation), but this method was also most time consuming and required approx. 2600 CPU-hours. Due to the high computational cost, optimization loops with repeated geometrical adjustments and computation of the corresponding sound emission is not feasible. In contrast, stationary (time-averaged) CFD solutions such as Reynolds-averaged Navier-Stokes (RANS) simulations are often sufficient for the aerodynamic optimization. On top of that, the requirements regarding computational grid fineness are much lower in that case. As a consequence of the huge differences regarding computational cost, it is desirable to estimate the impact of distinct aerodynamic optimization strategies on the sound emission without need for time consuming CAA. The aim 2 American Institute of Aeronautics and Astronautics 19th AIAA/CEAS Aeroacoustics Conference (34th AIAA Aeroacoustics Conference), 27 - 29 May 2013, Berlin of this work is to investigate the impact of four aerodynamic design strategies on the sound radiated by a low pressure axial fan. The four methods are 1. Straight forward utilization of blade element momentum method (subsequently called “BEM”) 2. Optimization regarding total-to-static fan efficiency (ts) at the design point (subsequently called “OTS”) 3. Optimization regarding total-to-total fan efficiency (tt) at the design point (subsequently called “OTT”) 4. Optimization regarding total-to-static fan efficiency over a large operating range (subsequently called “OOR”) The blade element momentum method is based on the two dimensional flow analysis at distinct radial positions. A detailed discussion how this method can be applied in axial fan design is given by Carolus3. The advantage of this method is the analytical formulation which leads to short development time and requires almost no resources. In case of an essentially two dimensional flow in the blade passages, reasonable accuracy can be obtained by predicting lift and drag of each radial airfoil section, e.g. using XFOIL as suggested by Carolus and Starzmann4. The main limitation is the inability to consider complex secondary flow effects which can only be resolved by CFD. CFD results are often precise enough to be coupled with optimization algorithms. The evolutionary algorithm implemented for this work was inspired by the work of Thévenin and Janiga5 as well as Nelles6. Evolutionary algorithms belong to the class of global optimization methods which is a major advantage as compared to gradient based methods. The main bottleneck is the slow convergence and the large number of function evaluations required. A collection of optimization work in the context of turbomachinery can be found in the notes of the von Karman Institute lecture series 2000-077. The presence of several examples with 2D optimization of airfoils illustrates the main problem of CFD-based optimization – the computational cost of each function evaluation. This can e.g. be overcome by adjoint methods (examples collected by Thévenin and Janiga5) or simply by relatively coarse computational grids. To avoid increased uncertainties, grid independency studies are usually recommended. Good experience with optimization work using a relatively coarse grid (around 500,000 nodes) was made in an earlier study by the authors of this work8. The three optimization targets of this work address different practical requirements. The total-to-total efficiency considers the real total-to-total pressure rise from a plane upstream of the fan (“1”) to plane downstream of the fan (“2”) : Vp tt , where ppp (1) ttP tt t21 t However, this optimization target only makes sense when the dynamic part of pt2 is recovered by guide vanes and diffusers. Otherwise, the kinetic energy at the fan exit is lost and the total-to-static efficiency determines the power consumption of the fan: Vp ts , where ppp (2) tsP ts21 t In some applications it is necessary to consider not only the design point but an extended operating range. Each of these three requirements is supposed to have acoustic benefits and drawbacks. Optimization regarding total-to- total efficiency is concerned with the reduction of aerodynamic losses that originate from secondary flows or flow separation. These flow phenomena are known to be effective sound sources and it is expected that noise can be 8 reduced by increasing tt. This is also confirmed by the aforementioned study . However, in most applications the blade load is determined by the total-to-static pressure rise that is required. The minimum blade load can then only be obtained by optimizing with respect to ts. Consequently, there are two competing effects which must be weighted up. In contrast, the impact of optimization with respect to operating range can easily be estimated. There will be a loss in peak efficiency but an increase at other operating points. It can be assumed that this leads to compromised acoustic properties at the design point